3.4-1 Use the definition of linearity to determine which of the following systems with input signal x(t) and output signal y(t) are linear. We use the notation g' (t) to denote the first derivative of g(t) and g(n) (t) to denote the nth derivative of g(t). (a) y(t) = ax(t) + b, where constants a, b 0 (b) y(t) = A cos x(t), where A is constant (c) y(t) = c1x(t—t₁)+c2x(t − t2), where constants c1, c2 0 (d) y(t) = ejwot x(t) (e) y(t) = Ax(t—to)+Bx" (t − t2). (f) y(³) (t)+2y' (t) + y(t) = Ax' (t) + Bx(t − to) (g) y" (t) +2ty' (t) +y(t) = Ax' (t) +Bx(t - to) (h) y(t) = √±∞ Ap(t − t)x(t)dt, where A is constant 3.4-2 Use the definitions to prove which of the systems in Problem 3.4-1 are linear and time-invariant.

3.4-1 Use the definition of linearity to determine which of the following systems with input signal x(t) and output signal y(t) are linear. We use the notation g' (t) to denote the first derivative of g(t) and g(n) (t) to denote the nth derivative of g(t). (a) y(t) = ax(t) + b, where constants a, b 0 (b) y(t) = A cos x(t), where A is constant (c) y(t) = c1x(t—t₁)+c2x(t − t2), where constants c1, c2 0 (d) y(t) = ejwot x(t) (e) y(t) = Ax(t—to)+Bx" (t − t2). (f) y(³) (t)+2y' (t) + y(t) = Ax' (t) + Bx(t − to) (g) y" (t) +2ty' (t) +y(t) = Ax' (t) +Bx(t - to) (h) y(t) = √±∞ Ap(t − t)x(t)dt, where A is constant 3.4-2 Use the definitions to prove which of the systems in Problem 3.4-1 are linear and time-invariant.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Consider the function given below. Determine whether the given function is causal and BIBO-stable. x(t) = 4 rect (t/2) Please show work
this is a signal and systems's question.
4. Plot the following functions: a) g(t) = -4 ramp(t)u(t – 2) b) g[n] = ramp[n + 2] – 2 ramp[n] + ramp[n – 2] CS CamScanner W al
7. A CT function x(t) is non-zero over a rahge of its argument from -2 to 3. It is convolved with another function y(t) which is non-zero over a range of its argument from 0 to 3. What is the non- zero range of the convolution of these two functions? Explain your answe. x(t) -2 0 y(t) 3
Answer (4) only
What is the sum-of-products expression for the following function. F(a,b,c)=∑m(0,1,2,4,5) a'b'c'+a'b'c+a'bc'+ab'c'+ab'c a'b'c+ab'c'+ab'c+abc a'b'c'+a'b'c+ab'c'+ab'c a'b'c'+a'b'c+ab'c+abc a'b'c'+a'b'c+a'bc'+ab'c'+ab'c+abc a'b'c'+a'b'c+a'bc+ab'c'+ab'c+abc
r(t) 10 + d(t) + a) Obtain the output C₁( s) whn r(t) is unit step displacement. Thenobtain the output Cd(s) when the input d(t) is unit-step torque. Assume that when r(t) = u(t), d(t)= 0 and vice versa b) From r(t) = u(t), d(t)= 0 indicate a. Damping ratio b. Natural frequency c. Final value of the output 1/S(S+2)
Let x(t) = u(t) - u(t-1) and y(t) = u(t) + u(t-1)-2u(t-2) (a) plot x(t) and y(t) (b) evaluate graphically and plot z(t) x(t) * y(t)
Find c(t)
A sequential circuit with two FFs A & B , two inputs (XY) , and output Z has a state table given below, derive the next state equivalent of b(t+1)
solve asap
DE only